Adara M. Blaga

Bio: Adara M. Blaga is an academic researcher from West University of Timișoara. The author has contributed to research in topics: Manifold & Vector field. The author has an hindex of 13, co-authored 90 publications receiving 589 citations. Previous affiliations of Adara M. Blaga include Yahoo!.

η-Ricci solitons on Lorentzian para-Sasakian manifolds

Abstract: We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0 and S · R(ξ,X) = 0. We prove that on a Lorentzian para-Sasakian manifold (M, φ, ξ, η, 1), if the Ricci curvature satisfies one of the previous conditions, the existence of η-Ricci solitons implies that (M, 1) is Einstein manifold. We also conclude that in these cases there is no Ricci soliton on M with the potential vector field ξ. On the other way, if M is of constant curvature, then (M, 1) is elliptic manifold. Cases when the Ricci tensor satisfies different other conditions are also discussed.

$\eta$-Ricci solitons on para-Kenmotsu manifolds

Abstract: In the context of paracontact geometry, $\eta$-Ricci solitons are considered on manifolds satisfying certain curvature conditions: $(\xi,\cdot)_{R}\cdot S=0$, $(\xi,\cdot)_{S}\cdot R=0$, $(\xi,\cdot)_{W_2}\cdot S=0$ and $(\xi,\cdot)_{S}\cdot W_2=0$. We prove that on a para-Kenmotsu manifold $(M,\varphi,\xi,\eta,g)$, the existence of an $\eta$-Ricci soliton implies that $(M,g)$ is quasi-Einstein and if the Ricci curvature satisfies $(\xi,\cdot)_{R}\cdot S=0$, then $(M,g)$ is Einstein. Conversely, we give a sufficient condition for the existence of an $\eta$-Ricci soliton on a para-Kenmotsu manifold.

On gradient η-Einstein solitons

Abstract: If the potential vector field of an η-Einstein soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. Under certain conditions, the existence of an η-Einstein soliton forces the manifold to be of constant scalar curvature.

Solitons and geometrical structures in a perfect fluid spacetime

Abstract: Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and η-Ricci and η-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector field ξ of the soliton is of gradient type, ξ:= grad(f), we derive a Poisson equation from the soliton equation.

Self-Duality and N = 2 String Magic

Abstract: We consider strings with an N=2 local superconformal symmetry on the worldsheet. The critical dimension for this theory is four (two complex dimensions) with the signature (2, 2). A Kahler function giving rise to self-dual gravity is the only physical degree of freedom of this theory. Some miraculous symmetries are observed corresponding to the exchange of worldsheet and target moduli. The open and heterotic versions of this string theory correspond to self-dual Yang-Mills fields coupled to self-dual gravity in four dimensions.